[jeffreyH (OP)]

I know this sounds crazy but a post by @chiralSPO got me thinking. Scale matters but is it theoretically possible to tunnel from one gravitational potential well to another? I have no idea on what the answer might be or if it is even sensible to ask this question. So fire away.

[evan_au]

In the quantum world, everything is a bit fuzzy, if you look closely enough.

One could imagine that if we ever get a self-consistent theory of quantum gravity, that there might be a bit of quantum uncertainty about what is inside or outside an event horizon, a (hypothetical) micro-black hole, or a (hypothetical) cosmic string.
See: https://en.wikipedia.org/wiki/Cosmic_string

[chiralSPO]

Tunneling amplitude is proportional to e^{–width of barrier}

https://en.wikipedia.org/wiki/Quantum_tunnelling

even empty space can be viewed as a barrier through which to tunnel.

Electric potentials within molecule-scale systems can have very high gradients, so the distances involved are small.

For gravitational wells, gradients are typically not very strong (except in the hypothetical cases mentioned by evan_au), so the distances are likely to be such that tunneling can only happen once every million universe lifetimes or so (not actually calculated, but you get the idea)